# Mathematical Treasure: Collected Works of John Wallis, including Treatise of Algebra

Author(s):
Frank J. Swetz (The Pennsylvania State University)

The Collected Works of John Wallis (1616-1703) were published from 1693 to 1699.

The frontispiece for this Collection was a portrait of Wallis.

Within this Collection is a complete copy of Wallis’s Algebra, first published in 1685.

The frontispiece for the Algebra is also a portrait of the author but in a more formal pose.

On page 105 of his Algebra, Wallis gave a table explaining his algebraic notation, where: quadratum, symbolized by “q”, indicates ‘raised to the second power’ and cubus, “c”, means ‘raised to the third power’. Thus, for a modern reader: ${\rm{Xq}}=x^2,$ ${\rm{Xc}}=x^3,$ ${\rm{Xqq}}=x^4,$ ${\rm{Xqc}}=x^5\dots.$

Wallis’s concern for the cycloid is contained in a contribution beginning on page 499 of the Collection.

The images above are presented courtesy of the University of Pennsylvania Libraries.

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Collected Works of John Wallis, including Treatise of Algebra," Convergence (October 2016)